Comparison of Multiple Lenear Regression & Artificial Neural … · 2014. 12. 4. · Sharifi, Omid Haddad and Mahsoo Naderi (2005), Paulo Chaves and Toshiharu Kojiri (2007) , Paulo

Quest Journals

Journal of Architecture and Civil Engineering

Volume 2 ~ Issue 5 (2014) pp: 01-15

ISSN(Online) : 2321-8193

www.questjournals.org

*Corresponding Author: S.S.Khare 1 | Page 1S.S.Khare, Assistant Superintending Engineer, Irrigation Projects Investigation Circle,

WRD, Nagpur, (M.S.), India.

Research Paper

Comparison of Multiple Lenear Regression & Artificial

Neural Network for Reservoir Operation – Case Study

Of Gosikhurd Reservoir

S.S.Khare1, Dr. A.R.Gajbhiye

2

1S.S.Khare, Assistant Superintending Engineer, Irrigation Projects Investigation Circle,

WRD, Nagpur, (M.S.), India. 2Dr. A.R.Gajbhiye, Professor & Head, Department of Civil Engineering,

Yeshwantrao Chavan College of Engineering, Nagpur, (M.S.), India.

Received 18 November, 2014; Accepted 06 December, 2014 © The author(s) 2014. Published with

open access at www.questjournals.org

ABSTRACT:- In recent years, artificial intelligence techniques like Artificial Neural Networks (ANN) have

arisen as an alternative to overcome some of the limitations of traditional methods .The most important

advantage of ANN is that it can effectively approximate a nonlinear relationship between input and output

parameters.

A case study of Gosikhurd a major multipurpose project Is considered. Simulation model is developed

for the Gosikhurd Reservoir for forty seven years historical data with 10 daily interval. Using the simulation

results mathematical model for multiple linear regression and for Artificial Neural Network are formulated and

the results are also compared.

The results demonstrates that ANN is a effective and powerful tool in mapping hydrologic parameters

i.e. input and output and is an excellent alternative for deriving reservoir operating policy.

Keywords:- Simulation, Multiple Linear regression, Artificial Neural Network, Reservoir operation.

I. INTRODUCTION Once the structural facilities like dams, barrages and distribution network etc. are constructed, the

benefits that could be received depends to a large extent, upon how well these facilities are operated and

managed. The objective of the present work is to study the applicability of Artificial Neural Network (ANN) in

modelling reservoir operation. For this research study Gosikhurd a major project perhaps the largest reservoir of

Vidarbha region, is considered.

The objective is attained through the following steps:

1. Hydrological data like inflow, irrigation and non-irrigation demands, and physical features of the

reservoir like Area, Capacity relation with elevation, FRL. MDDL and evaporation were collected from the

project authority. Reservoir simulation was carried out for Forty seven years with 10 daily intervals.

2. Using the simulation analysis mathematical model using i) Multiple Linear Regression(MLR) and ii)

Artificial Neural Networks (ANN) are developed . Which gives the functional relationship between output

(closing capacity/ water levels / closing area) and inputs (initial storage/level, Inflow, demands & evaporation).

3. Performance of i) multiple regression analysis and ii) Artificial Neural Networks (ANN) are compared.

II. APPLICATION OF ANN IN RESERVOIR OPERATION Since the early 1990’s there has been a rapidly growing interest among engineers & scientist to apply

ANN in diverse field of water resources engineering. Raman and Chandramouli (1996) used artificial neural

networks for deriving better operating policy for the Aliyer dam in Tamil Nadu. General operating policies were

derived using neural network model from the DP model. The results of ANN with dynamic programming

algorithm provided better performance than the other models. Jain, Das and Shrivastava(1999) used artificial

neural network for reservoir inflow prediction and the operation for upper Indravati Multipurpose Project,

Orissa. They developed two ANN to model the reservoir inflows and to map the operation policy. They found

http://www.questjournals.org/

Comparison of Multiple Lenear Regression & Artificial Neural Network for Reservoir Operation…

*Corresponding Author: S.S.Khare 2 | Page

that ANN was suitable to predict high flows. They concluded that ANN was a powerful tool for input output

mapping and can be used effectively for reservoir inflow forecasting & operation. Chandramouli et al (2002),

Cancelliere et all (2002), Oscar Dollins and Eduardo Varas (2004) , Haddad and Alimohammadi (2005), Farid

Sharifi, Omid Haddad and Mahsoo Naderi (2005), Paulo Chaves and Toshiharu Kojiri (2007) , Paulo Chaves &

Fi John Chang (2008), Yi min Wang at all (2009) , Amir Ali Moaven Shahid (2009),Paresh Chandra Deka and

V. Chandramouli (2009), El Shafie A at all (2011), Sabah S Fayaed at all (2011), T. S. Abdulkadir at all (2012)

are among the others successfully studied the application of ANN in optimal operation of reservoir system.

They concluded and recommended that forecasting using ANN is very versatile tool in reservoir operation.

III. CASE STUDY To develop and compare the application potential of the Artificial Neural Network model in attaining

the reservoir operational objectives one major irrigation project “ Gosikhurd project” of Bhandara district is

taken as a case study. The Gosikhurd project is located in Eastern Vidarbha region. Project envisages Reservoir

across Vainganga River a major river near village Gosi. in Pauni tahasil of Bhandara district. This is a

multipurpose project and is intended to cater the irrigation of 190000 hector annually as well as domestic and

industrial water demands to the tune of 124 Mm3 annually. It augments about 229 Mm

3 annually to an existing

tank Asolamendha during monsoon. Expected annual utilisation is about 1613.10 Mm3 . The Reservoir has two

main canals one on each bank.

Salient features of Gosikhurd Reservoir are shown below.

Sr.No. Particulars Gosikhurd Storage

1 Location :- Village/Tahasil/Districr Gosi/Pauni/Bhandara

2. River :- Vainganga river

3. Catchment area :- Gross/Free 34862Sq.Km./5902 Sq.Km.

4. Avg. Annual Rainfall 1200 mm

5. Water availability :-

i) at 75 % dependability

ii) at 90 % dependability

3407.688 Mm3

(Year 1966)

2987.411 Mm3 (Year 1996)

6. Storage capacity :- Live 1146..080 Mm3

7. FRL Level / MDDL Level :- 245.50 / 241.290 m

8. FRL Area / MDDL Area :- 222.965 Mm2 / 102.822 Mm

2

9. FRL Capacity / MDDL Capacity :- 1146.08 Mm3 / 376.092 Mm

3

10.

Annual Water demand :- i) Irrigation

ii)Water Supply

iii)Feeding to existing Asola

Tank

iv) Evaporation

911.414 Mm3

123.69 Mm3

229.00 Mm3

348.996 Mm3

IV. RESERVOIR SIMULATION Reservoir simulation for 10 daily intervals from year 1960 to 2006 i.e. for forty-seven years is carried

out. The demands that can be fulfilled with 100 % success i.e. 100 out of 100 years the demand is fulfilled are

arrived by trial and error by adjusting the reservoir releases. With these demands the simulation is repeated and

the demands are readjusted in such a way that all forty-seven years we as successful years. I.e. the contemplated

demands will be fulfilled.

The table indicates the abstract of simulation study.

Sr.No. Year Inflow at

Dam Site in

Mm3.

Total with-drawal

in Mm3.

Spillover

in Mm3.

Defecit in

Mm3.

Remarks

1 2 3 4 5 6 7

1 1960 8659.671 1638.0611 7000.41637 0.000 Success

2 1961 22924.428 1680.0185 20920.8123 0.000 Success

3 1962 5265.237 1631.0699 4089.54895 0.000 Success

4 1963 7381.389 1604.3668 5687.75594 0.000 Success

1613.10 Mm3



5 1964 7057.660 1666.6153 5401.8014 0.000 Success

6 1965 2126.345 1632.1663 739.736279 0.000 Success

7 1966 3407.688 1609.1428 1734.52484 0.000 Success

8 1967 6346.889 1598.2782 4597.5141 0.000 Success

9 1968 7319.847 1635.3465 5644.94399 0.000 Success

10 1969 8474.269 1661.8839 6773.99105 0.000 Success

11 1970 13070.585 1691.2407 11249.3698 0.000 Success

12 1971 3735.683 1683.8566 2382.35453 0.000 Success

13 1972 2898.823 1619.5789 1335.00724 0.000 Success

14 1973 10024.953 1594.1999 8122.73624 0.000 Success

15 1974 3361.811 1634.5859 1993.73695 0.000 Success

16 1975 9718.211 1562.2785 7899.66541 0.000 Success

17 1976 5945.324 1621.1621 4459.19713 0.000 Success

18 1977 7599.320 1646.9898 5887.85445 0.000 Success

19 1978 4419.888 1616.4769 2953.92336 0.000 Success

20 1979 3962.426 1592.4092 2390.89628 0.000 Success

Sr.No. Year Inflow at

Dam Site in

Mm3.

Total with-drawal

in Mm3.

Spillover

in Mm3.

Defecit in

Mm3.

Remarks

21 1980 5236.435 1612.1969 3555.74978 0.000 Success

22 1981 9281.757 1659.2779 7463.5755 0.000 Success

23 1982 3200.712 1626.0243 1835.85265 0.000 Success

24 1983 9061.437 1618.3413 7189.27253 0.000 Success

25 1984 3823.319 1607.6203 2442.60485 0.000 Success

26 1985 3584.341 1574.9845 2012.51944 0.000 Success

27 1986 3909.868 1559.7612 2344.02594 0.000 Success

28 1987 2367.553 1569.3123 869.535902 0.000 Success

29 1988 4602.015 1548.7985 2939.01549 0.000 Success

30 1989 2949.216 1588.5495 1451.00491 0.000 Success

31 1990 5985.780 1562.4623 4254.1487 0.000 Success

32 1991 3165.514 1591.5275 1737.59852 0.000 Success

33 1992 3599.793 1583.6274 1988.01048 0.000 Success

34 1993 7639.139 1619.4257 5829.33812 0.000 Success

35 1994 19985.717 1639.9313 18033.0205 0.000 Success

36 1995 3899.033 1641.7097 2742.49788 0.000 Success

37 1996 2987.411 1605.7791 1420.92026 0.000 Success

38 1997 4890.133 1596.6214 3197.32053 0.000 Success

39 1998 12896.004 1666.7905 10959.8729 0.000 Success

40 1999 8932.268 1655.9951 7387.07659 0.000 Success

41 2000 3196.757 1561.2142 1892.25826 0.000 Success

42 2001 3659.643 1553.1762 2072.32318 0.000 Success

43 2002 3576.713 1590.7572 1959.12625 0.000 Success

44 2003 9622.491 1631.2218 7738.37081 0.000 Success

45 2004 2316.623 1621.4485 1019.51363 0.000 Success

46 2005 11039.965 1611.7384 9060.04134 0.000 Success

47 2006 5860.152 1500.507 4558.93098 0.000 Success

Average 6488.728 1613.160 4877.007 0.000

The table indicates percentage success as 100% i.e. the simulation study is giving acceptable results.

The large amount of spill over is because of the inflow during monsoon season is concentrated mainly in July &

August and cannot be stored due to Level constraints and downstream commitments. The simulation study thus

forms the basis for multiple regression modelling as well as Artificial Neural Network (ANN) modelling.

V. MULTIPLE LINEAR REGRESSION MODEL (MLR):- The degree of relationship existing between three or more variables is called multiple regression.

Regressions models are formulated using IBM SPSS 20 software. The 47 years 10 daily simulation study is used

to perform multiple linear regression. Three regression models are developed. One each for Closing capacity,

closing water level and closing area of reservoir at the end of 10 days interval i.e. Multiple linear regression

model for final storage (MLR Cap.), final area (MLR Area) and final levels (MLR Level) are developed. Initial



storage/area/level , irrigation demands, non-irrigation demands and evaporation are considered as independent

variables. The summary of MLR models is given below-

ANOVA summary

Model Sum of Squares df Mean

Square

MLR( Cap.) Regression

Residual

79601664.48

6382408.48

9

1682

8844629.38

3794.53

MLR (

Level)

Regression

Residual

2660.991

215.075

9

1682

295.666

0.128

MLR

(Area)

Regression

Residual

2327402.078

185739.445

9

1682

258600.231

110.428

Model summary

Model (R2) Adjusted (R

2) F Sig. F Std. error of estimate

MLR( Cap.) 0.926 0.925 2330.886 0.000b

62.599

MLR (

Level)

0.925 0.925 2312.260 0.000b

0.3576

MLR (Area) 0.926 0.926 2341.805 0.000b

10.508

Interpretation of model for all basic variables and all readings: Of primary interest is the R Square and

adjusted R square values, which are ranging from 0.925 and 0.926, respectively. We learn from these that the

weighted combination of the predictor variables explained approximately 92 to 93 % of the variance of R.L. The

prediction model is statistically significant, Sig.F < .001, and accounted for approximately 92 to 93 % of the

variance. (R2= 0.925, Adjusted R

2= 0.926). In the normal plots the residuals look very normal and thus the

predictors mentioned in the model explained better variation in the data. Figure also depict the distribution of

observed residuals matches up nicely with the distribution we would expect under normality, then residuals

should fall along a straight line, as they more or less do in the plot mentioned. As deviation is substantially less

from a straight line, it suggests a fewer potential deviation from normality. Histogram and normal probability

plot for regression residuals for all three models are presented below-



VI. ARTIFICIAL NEURAL NETWORK MODEL (ANN) Three ANN models are developed. One each for Closing capacity, closing water level and closing area

of reservoir at the end of 10 days interval i.e. ANN model for final storage (ANN Cap.), final area (ANN Area)

and final levels (ANN Level) are developed. Initial storage/area/level, irrigation demands, non-irrigation

demands and evaporation are considered as independent variables.

The Forty seven years 10 daily simulation study is used to develop ANN Model. The standard network

that is used for function fitting is a two-layer feed forward network, with a sigmoid transfer function in the

hidden layer and a linear transfer function in the output layer. We have tried various topologies and out of that

the best results are achieved using 12-15-1 topology. Training algorithm used to train the neural network is

Levenberg-Marquardt (trainlm) which is recommended for most problems by various researchers. Software

Matlab along with IBM SPSS 20 used for ANN modelling.

Multy Layer Perceptron ANN model for final storage (ANN Cap.), final area (ANN Area) and final

levels (ANN Level) are developed. Hyperbolic tangent activation function is used. Out of Forty seven years data

33 years data is used for training and remaining data is used for testing and validation. The summary of ANN

models is given below-

Model summary

Model Topology Overall R MSE

ANN ( Cap.) 12-15-1 0.99 23.15 at epoch 12

ANN (Level) 12-15-1 0.99 0.00118 at epoch 28

ANN (Area) 12-15-1 0.99 0.9071 at epoch 25



Graphical representation of R for Training, validation, testing and overall r is presented below-

Values of R for model ANN (Cap.)

Values of R for model ANN (Area)

400 600 800 1000

400

500

600

700

800

900

1000

1100

Target

Ou

tpu

t ~=

1*T

arg

et +

0.9

9Training: R=0.99983

Data

Fit

Y = T

400 600 800 1000400

500

600

700

800

900

1000

1100

Target

Ou

tpu

t ~=

1*T

arg

et +

3.1

Validation: R=0.9998

Data

Fit

Y = T

400 600 800 1000400

500

600

700

800

900

1000

1100

Target

Ou

tpu

t ~=

1*T

arg

et +

0.0

25

Test: R=0.99982

Data

Fit

Y = T

400 600 800 1000

400

500

600

700

800

900

1000

1100

Target

Ou

tpu

t ~=

1*T

arg

et +

1.2

All: R=0.99982

Data

Fit

Y = T

120 140 160 180 200 220

120

140

160

180

200

220

Target

Out

put ~

= 1*

Targ

et +

0.0

81

Training: R=0.99982

Data

Fit

Y = T

120 140 160 180 200 220

120

140

160

180

200

220

Target

Out

put ~

= 1*

Targ

et +

0.4

8


Data

Fit

Y = T

120 140 160 180 200 220

120

140

160

180

200

220

Target

Out

put ~

= 1*

Targ

et +

0.0

48

Test: R=0.99976

Data

Fit

Y = T

120 140 160 180 200 220

120

140

160

180

200

220

Target

Out

put ~

= 1*

Targ

et +

0.1

4

All: R=0.9998

Data

Fit

Y = T



Values of R for model ANN (Level)

Error histogram and best validation performance for all three models are presented below –

ANN (Cap)

242 243 244 245

241.5

242

242.5

243

243.5

244

244.5

245

245.5

Target

Ou

tpu

t ~

= 1

*Ta

rge

t +

0.1

6Training: R=0.9998

Data

Fit

Y = T

242 243 244 245

241.5

242

242.5

243

243.5

244

244.5

245

245.5

Target

Ou

tpu

t ~

= 1

*Ta

rge

t +

0.4

1


Data

Fit

Y = T

242 243 244 245

241.5

242

242.5

243

243.5

244

244.5

245

245.5

Target

Ou

tpu

t ~

= 1

*Ta

rge

t +

-0

.12

Test: R=0.99974

Data

Fit

Y = T

242 243 244 245

241.5

242

242.5

243

243.5

244

244.5

245

245.5

Target

Ou

tpu

t ~

= 1

*Ta

rge

t +

0.1

6

All: R=0.99977

Data

Fit

Y = T

0 2 4 6 8 10 12 14 16 1810

0

101

102

103

104

105

106

Best Validation Performance is 23.15 at epoch 12

Me

an

Sq

ua

red

Err

or

(m

se

)

18 Epochs

Train

Validation

Test

Best

0

100

200

300

400

500

600

700

800

Error Histogram with 20 Bins

Ins

tan

ce

s

Errors = Targets - Outputs

-23.8

6

-20.2

4

-16.6

2

-13.0

1

-9.3

9

-5.7

74

-2.1

57

1.4

59

5.0

76

8.6

93

12.3

1

15.9

3

19.5

4

23.1

6

26.7

8

30.3

9

34.0

1

37.6

3

41.2

4

44.8

6

Training

Validation

Test

Zero Error



ANN( Level)

ANN (Area)

ANN network and important graphs for ANN model for closing capacity (ANN Cap.) are shown below-

0 5 10 15 20 25 30 35 4010

-3

10-2

10-1

100

101

102

Best Validation Performance is 0.0085193 at epoch 35M

ea

n S

qu

are

d E

rro

r (m

se

)

41 Epochs

Train

Validation

Test

Best

0

100

200

300

400

500

600

700

800

900

Error Histogram with 20 Bins

Ins

tan

ce

s


-0.5

335

-0.4

856

-0.4

377

-0.3

898

-0.3

419

-0.2

94

-0.2

461

-0.1

981

-0.1

502

-0.1

023

-0.0

5444

-0.0

0654

0.0

4136

0.0

8927

0.1

372

0.1

851

0.2

33

0.2

809

0.3

288

0.3

767

Training

Validation

Test

Zero Error

0 10 20 30 40 5010

-2

10-1

100

101

102

103

104

Best Validation Performance is 0.063561 at epoch 50

Me

an

Sq

ua

re

d E

rro

r (m

se

)

56 Epochs

Train

Validation

Test

Best

0

100

200

300

400

500

600

700

800

900

1000

Error Histogram with 20 BinsIn

sta

nc

es


-1.1

25

-0.9

858

-0.8

462

-0.7

067

-0.5

671

-0.4

275

-0.2

88

-0.1

484

-0.0

0881

0.1

308

0.2

703

0.4

099

0.5

495

0.6

89

0.8

286

0.9

682

1.1

08

1.2

47

1.3

87

1.5

26

Training

Validation

Test

Zero Error



Network Diagram Topology 12-15-1



Interpretation of model for all basic variables and all readings: The regression plots display the

network outputs with respect to targets for training, validation, and test sets. For a perfect fit, the data should fall

along a 45 degree line, where the network outputs are equal to the targets. For this model, the fit is exceptionally

good for all data sets, with R values in each case of 0.999 or above. If even more accurate results were required,

retraining the network might be possible. Retraining will change the initial weights and biases of the network,

and may produce an improved network after retraining. The error histogram obtains additional verification of

network performance. The blue bars represent training data, the green bars represent validation data, and the red

bars represent testing data. The histogram can give an indication of outliers, which are data points where the fit

is significantly worse than the majority of data. In this model, one can see that while most errors fall between

12.31 and -13.01, there is a training point with an error of 44.86 and validation points with errors of -23.86 and

-20.24. These outliers are also visible on the testing regression plot. It is a good idea to check the outliers to

determine if the data is bad, or if those data points are different than the rest of the data set. If the outliers are

valid data points, but are unlike the rest of the data, then the network is extrapolating for these points. There is

no significant evidence of influence of outliers on error histogram and the errors are almost normally distributed

which indicates better fitting of the Neural network model.

COMPARISION OF RESULTS : Results of Forty seven years simulation accompanied by Multiple

Regression model and ANN model indicates fairly equal results for all three output i.e. dependent variables

namely Closing area, closing levels and closing capacity at the end of each 10 days period. Further the results

for high flows (50% probability), normal flows (75% probability) and low flow (90% probability) are also

compared. The results are tabulated and also presented in graphs below.

Reservoir Parameters for 75% , 50% & 90% dependable year

75% Dep- Year 1966

Sr.No. Month Yc

Capacity

Regression

Yc

Capacity

ANN

Yc RL

Regression

Yc RL

ANN

Yc Area

Regression

Yc

AREA

ANN

1 Jun-01 460.706 473.000 241.646 241.620 111.283 109.970

2 Jun-02 446.213 473.450 241.611 241.610 110.702 109.540

3 Jun-03 453.216 494.460 241.655 241.710 112.031 112.010

4 Jul-01 601.485 648.280 242.419 242.770 133.613 138.270

5 Jul-02 766.294 964.450 243.332 244.600 157.292 192.470

6 Jul-03 996.705 1119.320 244.763 245.380 198.274 218.720

7 Aug-01 1142.426 1144.540 245.474 245.510 222.266 222.540

8 Aug-02 1154.032 1136.830 245.543 245.490 224.320 222.560

9 Aug-03 1148.791 1135.450 245.513 245.460 223.428 222.130

10 Sep-01 1165.430 1136.670 245.609 245.500 226.276 222.730

11 Sep-02 1157.709 1137.480 245.564 245.500 224.943 222.710

12 Sep-03 1149.122 1133.930 245.516 245.430 223.493 221.730

13 Oct-01 1136.929 1140.720 245.462 245.490 221.549 222.020

14 Oct-02 1126.038 1127.980 245.400 245.420 219.689 219.650

15 Oct-03 1122.933 1114.640 245.382 245.350 219.165 217.750

16 Nov-01 1096.063 1109.090 245.248 245.310 214.694 217.090

17 Nov-02 1082.508 1101.710 245.181 245.280 212.445 216.140

18 Nov-03 1069.079 1092.970 245.114 245.230 210.218 215.050

19 Dec-01 986.948 1055.060 244.656 245.080 196.417 208.210

20 Dec-02 1022.694 1016.150 244.887 244.940 202.574 203.180

21 Dec-03 992.656 977.570 244.728 244.750 197.526 196.920

22 Jan-01 955.852 928.510 244.533 244.440 191.374 188.060

23 Jan-02 922.867 884.580 244.361 244.160 185.831 179.090

24 Jan-03 881.766 849.370 244.141 243.870 178.912 169.540

25 Feb-01 807.129 806.380 243.709 243.510 166.127 159.760

Sr.No. Month Yc

Capacity

Regression

Yc

Capacity

ANN

Yc RL

Regression

Yc RL

ANN

Yc Area

Regression

Yc

AREA

ANN



26 Feb-02 802.750 739.310 243.645 243.240 164.814 153.910

27 Feb-03 762.930 691.090 243.373 243.000 157.463 147.810

28 Mar-01 680.644 666.040 242.842 242.710 142.812 140.480

29 Mar-02 697.038 631.850 242.917 242.550 145.296 134.510

30 Mar-03 673.970 605.470 242.761 242.390 141.056 130.490

31 Apr-01 619.135 602.140 242.417 242.280 131.419 127.520

32 Apr-02 626.748 579.210 242.445 242.170 132.475 124.380

33 Apr-03 608.084 561.980 242.319 242.070 129.055 121.870

34 May-01 512.652 536.860 241.751 241.940 112.703 119.720

35 May-02 558.341 519.980 242.042 241.870 121.427 117.680

36 May-03 547.469 510.830 242.011 241.810 120.820 115.630

50% Dep- Year

1999

Sr.No. Month Yc

Capacity

Regression

Yc

Capacity

ANN

Yc RL

Regression

Yc RL

ANN

Yc Area

Regression

Yc Area

1 Jun-01 859.663 835.170 244.020 243.590 175.257 166.150

2 Jun-02 831.094 880.810 243.826 243.930 169.988 176.160

3 Jun-03 890.040 1024.080 244.190 245.020 180.311 203.770

4 Jul-01 1020.305 1125.380 244.882 245.420 202.192 219.590

5 Jul-02 1159.838 1133.850 245.595 245.480 225.496 221.520

6 Jul-03 1161.527 1134.410 245.583 245.480 225.655 222.300

7 Aug-01 1162.771 1145.020 245.589 245.510 225.722 222.910

8 Aug-02 1156.591 1142.420 245.556 245.510 224.717 222.850

9 Aug-03 1153.873 1138.610 245.542 245.500 224.279 222.700

10 Sep-01 1223.779 1141.580 245.937 245.510 236.129 222.970

11 Sep-02 1208.408 1143.870 245.849 245.510 233.498 222.960

12 Sep-03 1168.399 1139.380 245.624 245.510 226.747 222.910

13 Oct-01 1176.588 1145.620 245.685 245.510 228.250 222.940

14 Oct-02 1137.136 1144.180 245.462 245.510 221.563 222.580

15 Oct-03 1126.450 1129.840 245.402 245.430 219.759 219.940

16 Nov-01 1124.700 1128.550 245.391 245.420 219.449 219.830

17 Nov-02 1124.700 1128.550 245.391 245.420 219.449 219.830

18 Nov-03 1124.700 1128.550 245.391 245.420 219.449 219.830

19 Dec-01 1050.185 1117.160 244.966 245.370 206.889 217.000

20 Dec-02 1112.393 1108.530 245.332 245.350 217.451 216.470

21 Dec-03 1102.773 1103.890 245.284 245.330 215.857 215.720

22 Jan-01 1085.440 1083.230 245.197 245.200 213.006 211.470

23 Jan-02 1065.237 1058.570 245.104 245.080 209.687 208.190

24 Jan-03 1035.893 1029.730 244.959 244.950 204.822 204.110

25 Feb-01 972.226 1004.040 244.609 244.800 194.121 199.170

26 Feb-02 981.240 943.550 244.675 244.570 195.684 193.120

27 Feb-03 947.376 906.370 244.494 244.340 189.982 186.190

28 Mar-01 870.254 896.110 244.049 244.320 176.837 184.710

29 Mar-02 901.641 882.780 244.238 244.110 182.176 177.540

30 Mar-03 881.628 859.450 244.131 243.990 178.805 173.120



31 Apr-01 829.375 825.860 243.833 244.000 169.952 173.880

32 Apr-02 847.358 819.610 243.932 243.850 172.888 169.850

Sr.No. Month Yc

Capacity

Regression

Yc

Capacity

ANN

Yc RL

Regression

Yc RL

ANN

Yc Area

Regression

Yc Area

33 Apr-03 830.466 802.780 243.818 243.730 169.792 166.320

34 May-01 735.793 804.070 243.255 243.550 153.567 160.960

35 May-02 794.111 779.100 158.528 163.254 158.260 243.422

36 May-03 772.332 755.210 154.551 159.288 153.740 243.276

90% Dep- Year 1996

Sr.No. Month Yc

Capacity

Regression

Yc

Capacity

ANN

Yc RL

Regression

Yc RL

ANN

Yc Area

Regression

Yc

AREA

ANN

1 Jun-01 514.825 502.430 241.816 241.820 114.899 116.200

2 Jun-02 495.549 492.810 241.758 241.750 113.705 113.830

3 Jun-03 482.505 490.140 241.723 241.720 113.072 112.880

4 Jul-01 584.680 509.210 242.325 241.780 130.843 114.350

5 Jul-02 612.034 531.460 242.435 242.130 133.651 119.300

6 Jul-03 624.970 586.340 242.446 241.800 134.019 120.820

7 Aug-01 677.075 1014.900 242.695 244.590 140.501 200.980

8 Aug-02 987.385 1124.390 244.693 245.440 196.511 220.530

9 Aug-03 1147.409 1135.280 245.505 245.450 223.190 222.020

10 Sep-01 1168.584 1136.820 245.626 245.500 226.812 222.790

11 Sep-02 1159.851 1137.970 245.576 245.500 225.304 222.790

12 Sep-03 1149.913 1134.470 245.520 245.440 223.627 221.920

13 Oct-01 1146.541 1144.160 245.516 245.510 223.178 222.710

14 Oct-02 1128.458 1136.260 245.414 245.460 220.098 221.000

15 Oct-03 1123.953 1118.910 245.388 245.370 219.337 218.330

16 Nov-01 1108.001 1113.740 245.307 245.340 216.672 217.710

17 Nov-02 1091.849 1105.830 245.227 245.300 213.993 216.670

18 Nov-03 1075.873 1096.070 245.148 245.250 211.345 215.450

19 Dec-01 990.859 1057.830 244.675 245.090 197.064 208.670

20 Dec-02 1025.136 1016.490 244.899 244.950 202.979 203.410

21 Dec-03 993.454 975.610 244.732 244.740 197.661 196.810

22 Jan-01 954.976 925.810 244.529 244.420 191.226 187.670

23 Jan-02 920.860 881.220 244.350 244.130 185.492 178.410

24 Jan-03 878.656 845.340 244.125 243.840 178.388 168.610

25 Feb-01 803.515 800.480 243.684 243.470 165.458 158.810

26 Feb-02 798.120 732.760 243.613 243.200 163.961 152.960

27 Feb-03 757.683 684.230 243.337 242.970 156.495 146.900

28 Mar-01 674.654 657.790 242.801 242.650 141.706 139.120

29 Mar-02 690.207 623.200 242.871 242.500 144.041 133.200

30 Mar-03 666.721 597.080 242.711 242.330 139.724 129.210

31 Apr-01 611.337 593.530 242.364 242.230 129.987 126.240

32 Apr-02 618.308 570.990 242.388 242.120 130.929 123.180

33 Apr-03 599.845 554.200 242.263 242.020 127.540 120.760

34 May-01 507.857 531.560 241.739 241.910 112.478 118.590

35 May-02 553.033 515.270 242.026 241.840 121.129 116.630

36 May-03 541.934 506.480 241.995 241.780 120.494 114.680



Where:

1. Yc Capacity, Yc Area & Yc Rl indicates reservoir’s closing capacity in Mm3, closing Area in Mm

2

and closing water Level in m at the end of 10 daily periods. Further Regression and ANN indicates results for

regression model and ANN models.

2. June-01 = June 1 to 10

June- 02 = June 11 to 20 &

June -03 = June 21 to 30: And so on for remaining months.

Comparison of MLR & ANN model for closing capacity

0.000

200.000

400.000

600.000

800.000

1000.000

1200.000

1400.000

Jun

-01

Jun

-02

Jun

-03

Jul-

01

Jul-

02

Jul-

03

Au

g-0

1

Au

g-0

2

Au

g-0

3

Sep

-01

Sep

-02

Sep

-03

Oct

-01

Oct

-02

Oct

-03

No

v-0

1

No

v-0

2

No

v-0

3

De

c-0

1

De

c-0

2

De

c-0

3

Jan

-01

Jan

-02

Jan

-03

Feb

-01

Feb

-02

Feb

-03

Mar

-01

Mar

-02

Mar

-03

Ap

r-0

1

Ap

r-0

2

Ap

r-0

3

May

-01

May

-02

May

-03

Res

ervo

ir C

apac

ity

in M

m3 --

----

----

----

-->

Reservoir Operation Schedule for 75% dependability

Yc Capacity Regression

Yc Capacity ANN

Yc Capacity indicates the capacity of reservoir at the end of 10 daily period.

0.000

200.000

400.000

600.000

800.000

1000.000

1200.000

1400.000

Jun-

01

Jun-

02

Jun-

03

Jul-0

1

Jul-0

2

Jul-0

3

Aug-

01

Aug-

02

Aug-

03

Sep-

01

Sep-

02

Sep-

03

Oct

-01

Oct

-02

Oct

-03

Nov

-01

Nov

-02

Nov

-03

Dec-

01

Dec-

02

Dec-

03

Jan-

01

Jan-

02

Jan-

03

Feb-

01

Feb-

02

Feb-

03

Mar

-01

Mar

-02

Mar

-03

Apr-

01

Apr-

02

Apr-

03

May

-01

May

-02

May

-03

Rese

rvoi

r Ca

pacit

y in

Mm

3



Yc Capacity ANN




0.000

200.000

400.000

600.000

800.000

1000.000

1200.000

1400.000

Jun

-01

Jun

-02

Jun

-03

Jul-

01

Jul-

02

Jul-

03

Au

g-0

1

Au

g-0

2

Au

g-0

3

Sep

-01

Sep

-02

Sep

-03

Oct

-01

Oct

-02

Oct

-03

No

v-0

1

No

v-0

2

No

v-0

3

De

c-0

1

De

c-0

2

De

c-0

3

Jan

-01

Jan

-02

Jan

-03

Feb

-01

Feb

-02

Feb

-03

Mar

-01

Mar

-02

Mar

-03

Ap

r-0

1

Ap

r-0

2

Ap

r-0

3

May

-01

May

-02

May

-03

Re

serv

oir

Cap

acit

y in

Mm

3



Yc Capacity ANN


VII. CONCLUSION The objective of this study was to develop ANN model for operation of reservoirs and assess its

application potential in attaining the objectives of reservoir operation. For Gosikhurd reservoir the optimal

releases for 10 daily periods were arrived at by trial and error and simulating the reservoir opening and closing

conditions for 10 days intervals. Historic data of inflow for 47 years were used for simulation. Mathematical

model for Multiple Linear Regression(MLR) as well as Artificial Neural Network(ANN) was developed using

the 47 years simulation study.

The research shows that the results by MLR and ANN model were fairly similar. Real time forecast can

be done. However, ANN has predicted comparatively higher values for reservoir filling ( storage built up )

periods whereas the MLR has predicted comparatively higher values for reservoir depletion period. ANN

presents very smooth curve fitting indicating uniform variation of capacity which is very convenient and

desirable by the operator. Whereas MLR presenting instantaneous and rapid variations in capacity which is very

inconvenient for the operator. The ANN procedure to derive the general operating policy for reservoir operation

gives better and robust performance. This is because the ANN approach allows more complex modelling than

the MLR approach. ANN is able to produce suitable degree of nonlinearity to match the considered pattern as

closely as possible, indicating that ANN has a great potential for deriving optimal operating policy for reservoir.

REFERENCES [1] H.Raman & V.Chandramouli (1996),” Deriving a general operating policy for reservoirs using Neural Network, Journal of

Water planning and management, ASCE. [2] S.K.Jain, A. Das & S.K.Shrivastava (1999), “Application of ANN for reservoir inflow prediction & operation”, Journal of Water

planning and management, ASCE.

[3] T.R.Neelkantam & N.V.Pundarikantham (2000), “ Neural network based simulation & optimisation model for reservoir operation”, ”, Journal of Water planning and management, ASCE.

[4] V.Chandramouli and H.Raman (2001), “Multireservoir modelling with dynamic programming and neural networks”, Journal of

Water planning and management, ASCE. [5] Farid Sharifi, Omid Bozorg & Mahsoo Naderi (2005), “Reservoir optimal operation using dynamic programming and Artificial

Neural Network “, Proceeding of sixth WSEAS Int. Conf. on evolutionary computing, Lisbon, Portugal.

[6] Paulo Chaves & Fi-John Chang (2008),"Intelligent reservoir operation system based on evolving Artificial Neural Networks", Journal of Advances in Water Resources.

[7] Amir Ali Moaven Shahidi (2009),"Evaluation of combined model of DP and Neural Networks in single reservoir operation",

Journal of Applied Sciences Research.



[8] Yi-min Wang, Jian-xia Chang & Qiang Huang (2010),”Simulation with RBF Neural Network model for reservoir operation rules”, Journal of Water Resources management.

[9] Sabah Fayaed, Ahmed El-Shafie & Othman Jaafar (2011), "Performance of ANN & regression techniques for simulation model

in reservoir inter-relationships, International journal of the Physical Sciences. [10] Ozlem Terzi & Sadik Onal (2012),"Application of ANN and multiple regression to forecast monthly river flow in

Turkey",African Journal of Agricultural Research.

[11] Dr.Bithin Datta (2012),"Application of ANN real time optimal operation of multireservoir system, Journal of Water Resources Planning and Management.

[12] S.S.Khare & A.R.Gajbhiye, (2013),”Application of ANN in operation of Reservoirs, IOSR Journal of Mechanical & Civil

Engineering”.

Comparison of Multiple Lenear Regression & Artificial Neural … · 2014. 12. 4. · Sharifi, Omid Haddad and Mahsoo Naderi (2005), Paulo Chaves and Toshiharu Kojiri (2007) , Paulo

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